{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Project: Multigrid Methods\n",
    "\n",
    "In this project we will learn three ways of implementating multigrid\n",
    "methods: from matrix-free to matrix-only depending on how\n",
    "much information on the grid and PDE is provided. \n",
    "\n",
    "Reference\n",
    "- [Introduction to Multigrid Methods](http://www.math.uci.edu/~chenlong/226/MGintroduction.pdf)\n",
    "- [Progamming of Multigrid Methods](http://www.math.uci.edu/~chenlong/226/MGcode.pdf)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multigrid on Uniform Grids for Poisson Equations\n",
    "\n",
    "We consider the linear finite element or equivalently 5-point stencil\n",
    "discretization of the Poisson equation on a uniform grid of $[0,1]^2$ with\n",
    "size $h$. For simplicity, we assume $h = 1/2^L$ and zero Dirichlet bounary\n",
    "condition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1. Smoother\n",
    "\n",
    "* Code the weighted Jacobi and the Gauss-Seidel smoother using the matrix-free style; see [Project on Finite Difference Methods](projectFDM.html)\n",
    "\n",
    "* Check convergence of the Gauss-Seidel smoother by solving $-\\Delta u = 1$\n",
    "  in $(0,1)^2$ with zero Dirichlet boundary condition. Plot the error in a suitable norm vs the iteration step for a fixed `h = 1/16`.\n",
    "\n",
    "* Change `h` from `1/4` to `1/128` and compare the iteration steps to drive the relative error  below the discretiztion error $h^2$.\n",
    "\n",
    "* Choose a random initial guess and plot the error function on the grid `h = 1/16` for the first 3 steps.\n",
    "\n",
    "* (Optional) Code the red-black Gauss-Seidel."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2. Two-Grid method\n",
    "\n",
    "* Figure out the index map between fine grid with size `h` and coarse grid with size `2h`. For example, `(i,j)` in the coarse grid is `(2*i-1,2*j-1)` in the fine grid.\n",
    "\n",
    "* Code the bilinear prolongation and restriction using the index map. Be carefuly on the value on the boundary points.\n",
    "\n",
    "* Code the two-grid method. On the fine grid, apply m times G-S iteration and then restrict the updated residual to the coarse grid. On the coarse grid, use G-S iteration or the direct method to solve the equation below the discretization error. Then prolongates the correction to the fine grid and apply additional m G-S iterations.\n",
    "\n",
    "* Use the two-grid method as an iteration to solve the Poisson equation.\n",
    "\n",
    "* Change `h` from `1/4` to `1/128` and compare the iterations of two-grid methods for different h."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3. V-cycle Multi-grid method\n",
    "\n",
    " Choose one of the following approach to implement the MG.\n",
    "\n",
    "* (Recrusive way) Apply the two-grid method to the coarse grid problem in Step 2.\n",
    "\n",
    "* (Non-recrusive way) Follow the description of SSC in lecture notes to implement V-cycle.\n",
    "\n",
    "* Use the Vcycle as an iteration to solve the Poisson equation, i.e.,\n",
    "```\n",
    "    while relative residual < tol\n",
    "         u = u + Vcycle(r,J); % correction form\n",
    "         or\n",
    "         u = Vcycle(u,J); % direct update form\n",
    "     end\n",
    "```\n",
    "* Change `h` from `1/4` to `1/128` and check the iterations and cpu time of MG."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multigrid on Hierarchical Grids\n",
    "\n",
    "We consider the linear finite element discretization of the Poisson equation\n",
    "on grids obtained by uniform refinement of a coarse grid."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " - Min quality 0.8507 - Mean quality 0.9612 - Uniformity 3.93% \n"
     ]
    },
    {
     "data": {
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2IcZ9F/Als06ygbSRrfYaPyDavH/1wFvPi1kvXOmQhWlCL3p+ztaNQAIjP3/V\na/qGntl5dRIamObSRibmIbPVJWtoqn2guxOFCnWX4zOZlsiu5+lK+QfPz0POwZVeaZSiXmyT/NOt\nk1ghzWB7e3t84cuo/5y8dcfxA45la31GgOiH4lYBfzWvP6TApgDouL5YnTRoDweHQ5vuBAn/Am+H\n3CbiHwrKvqS81cZA5QNXPm1hOtviqz9hnWREFEUbGxtT27/ZF2kf7ziewPIwdsgmf5IXQpBf4pBA\nuWcWPyh5fkejnqyTjFDamEBZJPMvGPZj10bCYnVhMBJt0sYeKxI5HxwOMZACqpfk3NgPS5XuYbNP\nuhBfjbx/kvzt7e3TJ+SskI6BZnXlSBiP31x1d2Gzh7aG1vVD1Ekvtj29B57wwnWSWxuJhCFp4fWp\naguV4tnbj6QMgfVse35u0B/iuC68w1MJDO9APA2vOOR595VmpVHCjET3shhAjBESNgJ4vWe20igr\n17t9bhLyoLxOL0IPTZXQeh652IQp+IrMv4DuPVofEyjcNqJidbWutaeOvrQlR6gA1yPsiYJ499kH\n/zd47pUr9UjMoD2MRvHpE3JWSFOEYdhqtSqN0jievNjYV9jsI4iBAPfCOslNE/4CdVKqNhLUQjh/\nq6+YzTajZT373+oOqA5E4Qf9x2EYnr6YxsIIw3Dw2eOdRzdb1w9Tu6qRJsFEldQMZdjsISPlyGiO\n4yPTfKOZ6x0mF0CkD2KWOssSc5vhXwBBOFI749FR2IxTY3qy1YVSeF3XGpm/leuxZzcpA5Qo3n7Y\n7OkF4vLPNKB9cDg8ZULOZd9TbG9vF3cuX66+NmgPx6OjF5JmF0J0drqg0xZJjaxS4pkRxppaBVQm\n696/u+w7izYCUNK9APeE3Ny+lj//dPjlk+6nCzCgG4Ew4Jvvf2Mtv3b/u39er9dfyLKnANvb25ff\nuhSUfSrUtl05jiedW12UHV8sXAADt42aGt4J+LzRjfCk+ylo6eXLOre6xa0remE0OiIgsd3boU40\nPo4nT+5/+qT76aA9fHjwuHv7AWrHPT+fke0bdyG276gfR/2R5+ee3P/04buPIX7PJs/15oS1/Pnu\n7RAV3k+HX9oOhc78HTZ78vUoIleK12c23IvDd/q/+2ffFKayex0fvvVRcavwxs3XxTlxyoScy76F\nSIxH+NRox1uADkcHDBn56a+XeGZERl8kezuhEdm1kdBGmWWEXkMMxppU9pcsQK0E9h+U/Oj5Z6e4\nQHYutFqt6PlnMNIh5w4JwXeEn1NJbjo7XSWKVWmUdQmUx8vKIIkFiQOODNGUgMoBLFNB2a80Sruf\nN1C/t7DMgDDFW8/X726hYlskHH2o2+7sdI9nPpX8sNmPeiPbodBrHwbtoX49ONds5AAAIABJREFU\n4pnGFZShtPgAHTMzZV/q9Ak5KyQhhNjb25MpPTISZKUCUymV2AgqX1EIlB3ZaYcW1klzaSORufhb\nhrGG2JPmkJ4QcgOH5+eKW4VT39meER988IE8IBWPPKPVBQo1XccYraiw2dNTI8TgQN+pm1Z4HB95\nfg7EBxjdIoQobhU271TRvQRKIcoARf24WLuSyhhkutE0Vry5Xx2PQFieQ1vC5n61fq+28+gmVBT6\nisJmH7vy/JzNQlU4R9BfaCwUDEq+ToEhkkGXMzM7Sr6NVFA2ucT0qykhNXg6wArp2D2iVxTWn8Wg\nu0cEnC4QYWVBFtohGQvoJNtBct/FNsvZCKVCSYaRi3Ze6A0cp89+XAxwjxTWH5vfQy2fMmBF6SfC\nFv7F+tQTqvv31Dm7+0qzc2ta9I+6g839qqx+FFBxRCoXnILZzKVZdElFJdsoJaWbLsJG1D4Ije5B\ngTESgI9UN9EqjXI4S0kuNF8qubsvvvqTUyPkrJDE3t6e3iRI2cWFl7WVG9H6QXk9o85b4Ek9l05y\nHyQHHN3sCvQKJRm2E5gdchxjdtlTZT8uhr29Pdk9Aox+T9SLxyND9YEQoli7QkXVQGen67CTZJIF\noimxEZR4fh46IIvEyn0/GXWSztrgJSNUbKBDEZT8oOQ7mEeOy/mcnCNwkma4aHuxsc9PJMS1ysHX\nfSngNAn5WVdIuvFIOEkyCYfQXVeDSqdMCiNtKSMy6qSFtZHQ+IxtsFUoKUuNR0cLf9q26uRTZj8u\ngFarJb76E6OE635P2OzbHqkQJ9SMiCQA4P5OPWmkZGenC2dICLF5pwqWLDIgiKs3VWIHh0Pd1VuA\n7btYKzgyoDNEq4nVRfE9heceu80y3kIe8AF3RzcU6H0VtwoygRPuYplz4Yuv/qTVajluvSo46wpJ\nia3LOEkyyRj30JGRjG7hObOpJ/wk2kgkfMbuzwePsNRg4MJOkjGOIeM02Y8LwOgeEWS/B/93dwKR\nUyUXPhBofBeF41rX29Ta6WBrJJMrXWI148ytk2yMdo4MqHIojFaXJxE2og5bCAHPqXWtTTURypbk\nggWbu0Mo1goUV3SYXEClUTod6dIzrZAc7hHgSOc64Ih76OsXa1dSTMKTzZl1nPATaiORRCGoR1WH\nseLIBmOYIhWpB/s02Y/zwuEeAbLfMzgcOlQXAKcq6fS8QhVxifo5JJMCI46IUNVdFCebXI5KV9tZ\nsOkkB7+qLY2kH4pUqyvqjdDKipoIFJGiJqJ1/XD/6oFcuSeEiPrx/tWDoLyeamWSf+k2ucQpEvJz\nP/3pT1/2Hl4aLl26VPnOr6aKBTq9s3ebouM6u0+DgEZQXjfewjFHOTvkW+y+0tz9vHFybQQ4avOm\n467nKZSYd1cgq029RdSLw2//xV/91V9l38npwKVLl4o7l6Hp3XYD5qRAAo9ZMCTm7OkPoyOZZwis\nPJ6f99ZzRoGnswPVZSZUNbF1GGdeuM8CblG/uzVofyKStlZHGA1qWL4v0X4riTHHiaZf2ThH8HFF\n/XgcH0GxUQAQFyiUY/Qz+pAS1omCu8jW8/Pj+OgUCPnZZWpINR4JcJKQd029ODXuocNNspDavj7X\nLaLSNALwQrSRsNN5LXaLoOxnp21FHCPLLYKyL77ab7Vap6mFMBWtViuKonHzb/BP4kCzgabJyXQY\nU24hiTor6sdhsweeHrdkIhi4+3lDuAlVTV+3ZyJUdZ8F4hHHs7uzY+WpA4KS32kfJ2lstN9CiOJW\nIWz269pSchsDDoL+XrBa0S9Idzny1vPFrYIcXVAYsMgnm+qz3siR8ZKJ7/b29m7fvm27cvlxdhXS\n3t5e5TspAQrAk2jtU2uviUZlLsgKQ2HsdzMGLXALIYQ+/eUky+oqxDhgJiMQpkhVM4hj1O9mdb82\n96t7W3tnSiFtb2/jGZ2azqQcSZZIwGBnuHmn6vl5XVwVKIWmWLl1ra14tDY1o+uk1LMAtYewIbGB\n2BCUfehgRNgcRKtGq0tpY6AkqK63jt9pYqUhrpBlhDQUUnGrkGoNo7O41WqttEI6o9RBrVbrL//f\n/xN8J1lArD/uP4H+qHx7EYdmOhHyduhJcyppROwCCwLjePJ0+MWgPYz68cODxwgXrOXPgw3l2eT5\n0+GXxomuc9xidoAsne2LV8xEKW54ft7NswJ8+NZHqU8cGWv584N/8Yn3lb9XLBYX2NXKYW9vb3zh\nS8TKUqmwPnzro+reRnHripslSAgBsal8u2wUVxkYBKzowqDsj0dHg/aQRFoeEatDvkvUHxkn0pJ4\nY+zyeDR5NnkuhADb0JPuZ9NJtUfPhTinUHZhoqtIWqptn5I+QBZtDMq213JrD9/9ge0DlDyw/MXC\nBZolbbwj3tof/eY/rd/bulx9NfXJQ4xZ0f/1rx79i3+5ubn4/OWXizOaQ8qYPVKgB50V7F89OOGM\niXE8kQlY968eoEkw+58r0Wp4MCBIRr0QSB8qjdJ4NIEJRi5/akrACDlXlH1Mp/td2Aa4AcSjPO+y\nna0/W/Uge0acO3cOlL7GZIwMWapTA61KNkURV+VKm10vN41loXvHW0ChEFgMRDJmTBFv+Dqt623P\nz+HRP46PSM5xPV0phMA8PZFhNIy8Z+PUSsCWUtXPxVwftbtxQl4KQr66YynOYshub2/P+9VfWOCJ\niVF4tlIfjJk4ISurN0sKbmMAAxzqBz0TQVk9GAhzdW51p3STyeLjeEJHN+qNZBUlpqkdq4qiCtoX\noo1EEga0kUwjzzGvNpou+6u/sL29/f77759ke8sPBOuIZcAdBQUbPX6GSDhGSIjZ/Khn4bB3F5rK\nJN/6iFjCjHiPjpCRinojqJ9Ko6SLt5A6LmAkTVM4JjmX6wvgYzlMMRog69BGuAy9wPIixnOBdKnt\nYYJ4IF3vrvVVGLO8X/2Fvb29FRXys+ghkfG4wN/CJDTaU7uvNBdeVgHqhYq1Apmucq0OFMaUQGWq\nfjL5NGRnZelUpTtSHx8UnlFFwRxG3fALIUq3OUkn1HlnxEnSJdxWjqg7/Y6aT1sAgMrb6I6phaZ0\nl7DZR9UDqR9k7xXvRyTq0J1chHjsft5wnFMZrWvt8eiIXCslWiAkOceC0KDuqk7F9XF4qDYnyfhl\n2c4sVJf8Za20k3TmFNLe3l7nh99fwL4mGAtYU6N5cwFMX0SoSnbcYiE1AqnM1JiYbVe0GTkG4q3n\noSArjVKxduWFqGRhOYHzltQbly3++/9wRe3HLNje3h7823+Z5cklLFaU8Rnqjq3JhyKVpRduCpwS\nesVtXUEXopnJccrkDo3UYCDOLJwP+SzYTDG8vrlfTT19crjSLbF6YNOmpYzRUYedEfyb/3gVhfzM\nKaSTuEcEXf2cxD0yRt5EckoRCj/5U17ZcxYnKcvOhRCoAx7HE8T3lTD9YrpTmE6g8ZG6wLKraz+m\nIoqiS5cuwedQoKsZhwzoHTm7rzTdjilMqJ1HNxVHyibexICASYCON0Wqxe33kHtE/3RcLD/3Heku\n+S3Q5FnZFPP8nC7ntHiWlRV16MhDK9+XIwsFIX///fdXbnbf2VJINuNxXihhjeyds7AN5aysSFIm\ncmJWJLaPyFbxmQWKylzMSTICFjFWxlNDDtMLKfyC0+ut5zKqWFmJzjsdw4FT7CRtb29Hv/gjmyjK\nOh6Pb4cVJVvfGQMAnZ0unBjMylICy0ISb5E8TzHI3C2H8jPaUUah61ebxlUCv1l65vSgtCLn8psl\n5tag5Gf50GiTbpNL//ocJsKgPfQGF1dOyM9QUUMURa1W64U8guW2Ic/PU/efDGOHNtmGSDUL4ah9\nmqaaM/Y/uaEPsMDJOSEvkUh0M21VJBz+YjaTLEyxPpFWNIFme0RO6C4nR6VR7mz92Smb/SyECMOw\n1WoZ3SMAZlNnp1u/VzMO65JRaZRbvTZKD+TCB8Am3uOExwEsRE6Pqg81M46PHNT4g/bQW8/LxEIo\nu9BNE71LGuE4vXtJ8RTd9QUisTjxW+o0csv5lB4wHpJmEhY5p02CYMJh13rJ5LBpe5Yzdh2U/PDe\no5UT8jPkIbmNxwUAwwrWX7F2JaPrkwWy0eTgXMkOYxzghThJ2YtTFcgGppAi9YojhVA+jO4XUi4B\nrKj96MbGxoa3uZZqYeDxStUEDlC9tbeex5BW4RRvxNagltxiIPu77sJ0XXSNZRc22dNfN+ZdHE6S\nWlSdpglE0pYwjidEx+CWc/QvjkdH2frBD0G6kRotGLSH486zBw8euC9bKpwVhYTYuswdOc7G4e2+\njLKyyuE8YdZHCa/NS6anwJHdTY1xu6GcbUc4JSOMYRCRfLy2v5rrdpSfG//F/3OaMklhGG5sbGQZ\nK0zBpfQrJdq6LOJNysM4nkpGxn4mR1uPohhsSVzF6kKXkvFKY/XBAv1DVBfuqBQVQujV5yKbJOPP\ns3/RDx48WCEn6ayE7DARRz6H2c1tIvIyLNsUIongnXCHBH3uGcIsbpoWBxxsRuhQWUwh6VRyXjKC\nbOFPQw+D0FxdBxE18YClQiYYjaLogw8+WGmeFRlRFAkhgvJ6lkcVpkKk2uOen0OpgkB1mfNxiaJQ\niKjcaWS8Umj9TBRLnLnSQkDuJeOC8BaMk9TpSswOP25OulszXmns1tL9ITfdotylZIuKU3+YmHId\nTeDGZTQ6Ed8rbhUczyUA7BUff/zxCimks+IhbW9vhz/68yxO8VyAXZYa/F1gTb0Sd7HwWmotwMJO\nkiMMeBInSQaO9+Z+9UXVXxCQPRY/OL9aAQ0HEJHOwjaLCoUsgTUhxP7Vg/rdLRRSur9WvWrGdi5s\nldBKSj9VdKnUwl3jSmcnNaSsbMxWVG1zkvSe2dRjS66e5+ezCDk+Inx9qQ+c/asHxVphtYT8rMxD\nCsNwc79qo6ZeDFQpkHHOXhbYxkJTLnfeBZG7dlxQaZQW2HnrWrtYKxhJml/Uh0zHm4gbTr4mkFD6\nX4FXcToQhmGxdiWLkEBu9ZHkxiuR6ijWCpR7N99d81Fs58JBh6+MQXKQOAB4C+5J6iLxVFAB6FbA\nYPXGz47hKeQkyS8aGRzIPzPeTg48epb5TDLwW0zaTZ3UjBO6ckJ+VhRSFEWwKRaeSq4Dh1DYz968\nwAPCZvjg+M11C6VCyQjj6UpdVtg9Qsxpzpiis0E53pVGKcus9CygB43n56IoWq3j6gAkHELi+DZJ\nJLzZkeTmiyWV4NZJYbOvy4Nnmj/psJC8hOVIpJEP4aTAA0ODLebg2f6L+jHeOM1yNS4rj4hEcM/2\nydA+6U3p2ii5skwpIuUtKPHASqPknphMI89TtRc+vUqjvHJCfibYvlut1o/Pf3q5+upa/rw4J7q3\nH2Tn+bZBIfZey5/3/PzT4RdRf8FMjxCie/vB5eqrNm7vhPk4hY95ZsG3Q0QD3Jd5fi6VTpgwxtyH\ne1sKcbK8z2eT50+6ny5MUq4bm6AA95zsyJkXv7+5X8U6UW9UeX3jFNQ1yBIelP0Pf/ujy9XXjF9Q\n9+2wuFUAk7r7m4p6cfhO/833vkGvXCxcMHLeh82e5+eN3gz28/DgMRjHU+nwPT//bPIcLN1v3Hz9\nYuHCOJ48mzx/cv/TJ91Pw2Y/fKfXvR0+uf8pRR3Ho8nFwoU339ss1q7Y/lvLn4/6I8/Pr+XPR71R\n1B91bnXBXP6k+ym4wPFbcU48PHg8aA+D8npx64pjn8RJj93aQotr+fO4i/Ihf/jWR1rc8pyDLHwa\nWqctnRMPDx7bPEhMmF1FIT8TRQ0ff/wx/VysFaJebEu3ZoceT4A9aJuzl4qxNM3MhmnuN9vguyxz\nB5Jl89nH4mFkuDtFRP1DC+hmm7FpG5I27+JCihcF5fXVSvna8PHHH9M3InerKJdFvTjqx/Jn6+AL\nHrQNBQXGOXt6l5IMT5o/OWgPlfqacTw7mG5E7U0TkRRtewlpFjL5slDttw/g57kFEoyrYbMnV4SK\nhB9oWup2vS0zpHh+YdAeypMJxWwVHDlJqf3aOjWqPNlP/qCKtcKgPTSyBYrZmAQigcYjpoTTV0vI\nz4RCErMx6xMWrQHKwQY85+xXN1KTPQAUqqORkDA4tEb/FOCoZ3ncKw90x4IIc8/7CYPO2Ry4t0zk\nzA69LDAo+eF/H56CQrswDIs7l+mfNjVjrPhCzYjefG2rj4BQkU5yVLgJ6bmPzichRNjsj2915YLy\n6Q/SJO9pZXN53d3xgyhcsVYYHA4dba1Jzqwg83B7ySBXpa110P4kbPYp7Dkt0U7I7JU9UwYLqstO\nhz9T6ecoI4Ilp3+GsAKVNRHHVm5KeSZ6ZbWE/EwoJIWgwUsj5E8FpND4q8V0Uhb3iACDy/1odofg\ndRhp8/U1M44MFwvpD3dVFU71AkqOAGqA2TXzUfQXi622VIiiaLP0G/RPm5oxfn3Gkmud2kOGrJNk\n9yiVGcvzc0F5vVirCnvPDcRsc7+aalFRUTjerE3aqe3Bfeqxn6g3woPeWLMjJLUE1UV7Jh9L7ngV\nifVGTpK7qNVYKW5rxdW119g0Rnm1hPz0FzUgoadIP819WXBNy9BlAI8DJZfrRkb3iNav393qSGam\naUFDktm9plxiZAQC09kXzFILRMhCVWfLD2cBojp6kGT8k79Bj9rqAvtXJJzUDL3i0DEJKc5M6YHb\nmqk0ykHJ332l6fm5zk63da29+0qzdf2QRKjSKO08urn7eWPn0c36vZrn54OSD5GgbjPz22n2N/er\n+pYUyNV69Bw3XkbdUan1O9TPC7Yk4zXYvOfnot6ofreGxTf3q/V7td3PG/W7W1AeqJ3p3OqiqgKB\naHxcaR/sTNWro4BIf9dG1eX5OfHVn6yKkJ9+hRSGoc07Job5uQARd8esoZPA+pO6oLu4zra+Q6Ei\nVTBva1FQ8sejI9sHssDcB5B/Z/mEo16chTjV8dxJX7+tjtOerrmeX6EaJCOiKDJ+16gZo4/LrWMg\nrknYylqcCVkNmz2UruHF4lah0iiR7sEDHYV89IcwuRA6cxiCsmevVIErUHpmbd0Lyrt2VLJBSCCE\n7rMgEnKgoOwr98WLxVoBKmrn0c363a363S36MAft4f7VAwRUjSvLWhPBOkdwXr67u/Z1VYT89Cuk\njz/+2Hi0PD+3eacq125mxOAwEyEp/JgsflKWhJAOR6G57eHrhsOnccv6AgvKmE46yEbjvVjXlDxS\nUwFSvvMuuFRwSXhS2O3o/qGLyaNSCnaQUAmbvda1duv64eBwOvO70ihDwaQGZhUSB0f/k+zZy1Xg\nCqC3dAIFZVldsyaFZwZNo8xddThJuDuOmPG+MuBO4aERlPxKowT9NDgc7r7SNConilWkFhCR9qIi\ncstl6x988IFtkaXC6VdIYRjayFQWCNzB+cjoKGSJ3S3mzQjJCVNOF077YmxARp8m1Uybd0EZWZj/\nZVBBYPY9dHa6DmbboOSvSjTDhjAMp/PukoIx+hWpmajnCjIDFCWL+nFQ8kkJ7V89gFZAFA4+EAjr\n0JyEqJ1rh5Kb4uh/0hOfthNqjEjrxooeCbeFpvVGb7knSQbyNLJ9g7djeNvS4njXyE4hvAH/afNO\nFeoKkb1p4VzJH4+OQJqV+qjB28EJVShoYUnA8V0VD+n0FzWgYdD2W9QjZc+9z+t8pNY4IGKefUFl\ncb0KfK50lHFBpXAgS523e0Fb/d682kgkD5TspQ3Q986i5JM2Nr10RFEUNSOwosl0tEIIJNjHo6Ok\nzi3FuUQtnOfn9q8eJAQNpaBscF5llwszjWxWi+we0V2MzHVGNaNXDNoKdhSWOVvgUS+30SvThL30\nVH/0GysRCKSN9B3CeQrKvmgc14OEzT6+xHE8Qfm+vqaC6YSL8jp0mEyeS8OZTtio/nPDKfeQWq2W\nm2tyqjAyB+4GyVjx7CA/Sbe2FnaPCHpQft50lAL4NCS+0ymZJ6iPt4XjF9BG8g4zXuwI1gGrlfLV\n0Wq1UH9IRvc0l3N3a/NOFc0uqKjO8kiiquudRzd3Ht2EJ2S8UnG5MLo+SxYnuV6tWbCpGd2jchTs\nyCE+BzGrHI6Dx2O8UneSEtIpdZM2J0lnz7OVDiUZqXL9Xk2OHBrfpozpGM9aQSTJvPrdLcgA3Fn8\nalUiAaecqWEwGPzlFz9wUwagX33QHqYyCwzaw7XceTe/lu0WQdnv3g4VroHOzv3Kt8tom18Ynp8P\n3+mhwbuz071YuLAwRYJIGsujfny5+mrUix+++7h+b+sk21vLn1/Lryld5dBG1Ew+74JPup9l6flt\nXWtfrr7q6LcHxqOjc3/9d1alc1DBYDD40bPhGzd/RSZQWMufB3XIxcKFi4ULUT9ey609/eEXb763\nGZR9x3/j0WQtd/6Nm693bnVtXA/Ah299JJM42JhK4EgZSUDA4EAnorNzH9QM+pUQIbxBnT9CBjF6\nRP3R0+GXNkqItdwacSJ8+NZHiscj31cmRMCtf/fPvmm8kogb6EUjux1u7fhsx/GkezvE5OVirVDc\nuuL+ygbtITgmqr+/gXekrDwNMJ4TKyHkp9xDsuV7FWQhmhQZamEdSAy9PhlcJ3ePaGWqAj+hewQQ\nGd1cdd4OKE4SaaOFHa8s1HbGOIxteythPBoBCXdnQ0EqmoWgdnA4xFJZqFSVFz0To6O7Y++Y7KA9\nFCbPg4CKAMzCyEKQ6iZmpdB0aqO3wm7nOA6Kk2TURuK4ne4T4yIywV0qtZ04rlMv2WIGlEBdFSE/\n5TmkMAw3f+83Ui9z9KsTshCVZrlLZ6dbESIo+yfJHsnAU6NYK+xfPZiOp5Sm/iy41fU8uOs9P59x\nmJtrNSmTdHJtJNJm0gB6h6B9e6vUOaiAJNxB14RvkCTcEYUj/hHoBtskkUF7WL9r8Juhk8JmLxl8\n3rO1lwKkR8fxxJb4JKWIMopxPIFbYFtzHB8hiYJco+OyqB+P25P63VrUi3VmoON3tFWgwdDuMkWo\nfKTHbFyrImmS1U0lhW7V8/Mw42w3HccTN2mTnEBdFSE/5QrJXdEgw7MzgAGpZPgZ70Jd5UrE3Ejq\nRaolmTKZXJPkrsXsKRqPjlKtqiwgrhTZTDayvIhpbjaf/MrM/QUmiKmFezJtBLi5jubqmvISRuRV\nIaCUQRIOR1mfqUNZT2MJjHKlrBVIJ+kLIlVuXIQKFkLRU0gckh9mxBvzUsfxZNCecgvZeHpoZHBq\njeWUryjbZfpNdTlHiUFQXicNZ5RzHG3YcI42Bi/h6g60cglZaD07tR1dT9VG5gVnC9lXQshPs0Jq\ntVpzBcQcRJM4Nhl7ZVIRlHyqZXI/7o8f6DCa7FSPFH94IZucFlnNcpwYnyn4Jx1+B/cXPsOThygB\nB7lk9mCdvNryn1UdioRTu7RiVJGcuJmFdWIhI5VqFstMrtZT9qCIt+fnxu0JbT652KzwiOkgleAq\n9TIUQ49HR8b56MkPRyKpYfOmxEKxes2saUhejtt9RzhONqeMdKtGajtApwlWsnfGQvblF/LTrJDm\nbXh0BO5Okj0SyfRMsHvRwRsnM6RPGBCjHW7emeaoTuh/wATWp5vLLlH21ei4wtlCnGFMMRB7BMkN\nz0IuaaTzSsVqMSITZJJvwFgkLX9ENmZhG7GQQqWq84UDuoST0+A+OFEvFqKfhbkOZ7BYK7iLMykS\n7iYLRg0ezDi94Fv+IWz2p5JW8oNGSv8v0njjeBL2pkKuM5QLLRxnI7izFZSDl0imvoSNKxrHF4xH\nR5XGzNe0EkJ+yosa5n3YeRoDGLBAsQCG6RHHlxAiKK+jHNPz8zhaqbT5GUH5LVtn+3yrHQ6nUyzn\nbEE1Ytqp3v4kKPlByQ/K6/V7tfrdreJWAcqJmtXnvRfIn5QXbUyUbqxKyldBFEVKmaJeJI0uV/kC\no5A4TC4wMsDXkcN6DgkPSv44niCN5H4LKFJIZa4TxyrT1RlNhULujmxqokplEpHZ7VLraAaHQ7Db\noQQfQg7loQg5heNEGt2qkZpEHx4IDUf/NJYjrYSQn2YPSSH5zgjKdpAGcjMfy4CdKIRAvKJYK+D5\nq1wGb8bz8wsPDVJAUZQs2f6UpaSGxxcygkhINOE4nKIhPD9HzP8I5VGkBT6Tg8yfoNuPi1EcidVJ\n+SoIw3DnDwzs3XI2VK9JQc2VHNlLLdghP4m6NSHhZGEo19PEh3F85Kb5oKo51PvYhsLMkA/ZxZJW\n8xIeE/NqyXmxpXMAmd4eNX6OAh9itwv6UzIXt5CjX9WtjYTpRFtpguMJtmdLoK6EkJ9aD8lI8p0F\nJMrHPPNO8jqim4SdiD416is0PhxRKUTl2vPuUIFSPp5K2u2GnCFIpZjMCEquen5et1vxAN3cr4Is\nOSj7US9uXW+7OSgB2X48CcWRt4K030aSb4DaGGz0AZVGeSxNOnenhagjgoYbiUTCN/erRgknOnz3\nSHW5KNzmuh3vsHYslsJC6iO/X5uTpHTgOm4q13lDi9h8uBl2u5KhCNAk5CMksaCljMsC8ol20ASj\nwtaRQF2JHvBTq5BAYadQe2WEHLgzktcR3eT+1QOim6zfrRHTl0MRymfGc5J2Z4QioLbjmgXKWfXm\nHCFhhJxcxft18Czo59bBQSnEDLUdtNECJghMS7E6jMhAFEU2CafA3eBwaPxAlKe/XmxilHA8lGkF\n28ZgzFHZAphQjMdQiYTbuqkUKlXPwkenkGbZpFcherDFAMnjoVds00+Ujr3UWLfn51Cbjt2mCrls\nF7ppggftoZF1gnjtxqOjJRfyUxuy+/GPf4waaJ3ZScwWrRm99WKtgMDdOJ5Q6AO9C3LmdoEKZhoX\nltzoSmene5KR6opC8iwcXNn2ppKypEYqUvcmZu01JKWzvFmKeCQzET4ZHA6nVEYlH0rOS6jt8KQw\negNJxfzReDSZ1geSBpIKqFYObgmfBqP6cVBeN3598tOfwkpuCUcZN+LS+1cPjC1KQoioN6PePAtz\nnTESbuSWtImlctlAG3GpS69elGE8L3h2Kxu2lRjoaUvoBuOTAX68EAJrgMHQAAAgAElEQVSfZNjs\ne+u5+r2aW8jhdemsgPKynp8Pm/2pX9iPIeQKt6EQ4sc//rH+58uDU6uQhBBByacntfJUonEj1sPs\n54tbBUoODw6HdERtdJNZAHtWFinvuDPpygJPRmMn/GLTvo0FVBSpWCAUhrOnpPGI/z/73vCxVBpl\nlYPyVlcQ+V57kgRaj1WOfBpRbUxzS/Ghef6xR3VCP/WlwCbhQnKRo95oxmWZtcmIIqF1re2WcHoQ\nQ8EIIdBOp9sWUT9W2mb1vKzQLDOAjgNpO2PHhaeR9hoPgi69xm505bw4CjX10lOqepAvs5Vrowyv\n0ijhemyPEk7CIuQyQSrxQaQaVUjEKgX0nZ3u1772NX1jy4NTq5C+9rWviR8e/5M0jfFi/TBPn2jJ\nV755p7qwEpJhjOnjdOkdiBkXtA2lntdJsjFH0PTleWGkCaeo3cLV3p5EkBz148HhkIwGLxlFajyN\npwxuCffWc51bXYTm6DkrNJsMyCLhiv6oNMrwZlq9thwpNbbNehpPhKOMQvGobOV/ihYxHgSRSC/0\nsa1mnWresJSjUFMpMUCRjvEAKpUIMM7Go6OdRzflDwcaTq87V4Rctoy9ZGStYlSBAwWfzMnrpF4W\nTm0OKQiC7NkjkgCUBm3uV3HGjj39RSdnK7B1hhJV11yrOcr/5q1HcBDreQvNaXWwhBmzvguAYvEC\nH2B5HTl2lCkH5ZSpvqsOh4Qfc9euHxeFy0JeaZTBKDolcVjPh82++7wonr1I1ExQXm9dPyTRjXqx\nsT7CS3gi8E93GYVcBW7ruJBTRHCPbNkyOlkOHjxqITB6PDNXSukrlF+bD6BE6xD14v2rB0F5XdFG\nAuXa9qIPgBJ4np+ThRwchvKC3npeIcxcOZxahXRCTNmo7m6hFk4IsX/14IRfMyInNuOl0ig7BjYb\n4egdmbcewU2sN++c1kiaBq3jhXQ4jeMJOmNgnyLVtMAwWXnBJW9izwjKsbvN5EF7SGPjK42SolcU\n2CQNYla/u0VEIY75LLC6kCJK5exAANahaYRUR+duEySyYMfgSlhdrWvtVIZJMvWM5dcEaLhxPGld\na3dudet3aza16ijzkTUZHkeOaZ/j0QRKy1FFsvxCfmpDdicBNAfOKr7XSqOMXuignz550wYl2auA\nCp8yBu5Se0eyZ5JSiZHmbW9KnULkyPpmgc6JF5R9TN+wDUJMhdxXuLqAnq7frVFZIzE8yYh6MWkj\n6A+E4BCb1T9AfNq2m8JoQ+cDsh2iL4SJ6QoBNLCPizT+RpGoNyT5Fb5E/BNel7tNEE7S/tWDSqMk\n31G/HZqIqV19um3Tu0AtCfQE/bn+LsBQ7GbzMpb5wLqK+jG+yqgXo3UJkU/h9OG8hNVQrzpZfiE/\ntQopCILFPn3ZchRJdT9MoU0/764vckNP9qp7TgqfslQQpFKKeabxr0ZkGTKbvXJPJ9EyrGYn6XJD\nLlLCKzJ5qHs4byqW3HhUoEu4oo1s0Ecj4hmKBxkkXK5W0Ctx5DtG/RgD1EXSnkm15jLhm/xPIURn\npws1g3+a+RtL/iCetmnLhUi05nGnYDzMEgwIm32JHXV6x+M9+DnRFzjpYH1Nsm7Wd7H7SlPesPwu\n6M9RAoq8jjkZpll76MOrNEo7+wk17ei4jL5+dytVyD0/t3mnatRJSy7kp1YhLQbZciSQjYlHPCzx\noLw+11PPzZFMcBC8KvvMQvaaxUlCKEOpl11sKZGZ2FTP+maBjSxcfqZkMSFPJaCqFW2ENJt8ma6N\ngvI6XQMJV1wlRRqpBmyqhNbzQXkdX8ruK03ETt3UDGGzJ9cH2gDGAfdZoLCeezWcKTexHlyoqDdK\nZa1ERaJ7NZhlZIOi+obquRXlJFOjQsiV7xE2MX4mw0thtZCvEQkxkm2AyNLiNOeQ5m2JxVlVnvLy\ncQVI+mWu7iyLZ5le4WlcZEY40rPKaqkVBFncI5EtKTW2T4PWIWd9U4FYfNQb7Ty6qWijqBfP5HX9\nnDvU7rjFkhuPOqQA1MRRG0aYSrhWkw16EYKSN8WzElmT1rX2/tUD1CZs3qlSJ3hQ9qE5oMMcHz44\nF1ITfgk9aNmdbkRJN7I1jtVwXly7ag+99TwGDKaUGLSnXfCoNXBcg6GI0BPFZMD85p2q5+cGh8P9\nqwfohEU4DmkCSovqnfgyaaGnTfs0oqgNWlx+IT+1Cmnez123HKfraMdVHBuSBUceWF1/luPSAQq1\nO65JdaEIlNF1LpUy5BuYdvzYl9ItdAeM1KhGgC/AyJkGGAlG560QWTnIEm7TRijiws/HpXeavawH\ntyGEm3em6fHOThdKqNIogT4VSkj+E/i7XsK8ZeU/7ceo8ZPZuXRQM6yLT2iqRVIqVOFCFWsFh26D\nWeZZOCAI44SeykiCpVwjNB4vxAMrjTKoV/FdhM0+PuTW9cPNO1YqJuXpoeskRWkBeOOLhcdfCk6t\nQhLzVH4bLUeCLReF+qKoN2pda6caaFnidQQcHtsZc4yF1uE5ObjcVUxzLZU6DVpfLbXWTnaMbCE4\no6bPaEKuOiDhxlE6CpCWMJbe6U8xHfCZdCUkY6BNAjReI3fX2h6UY2l0lqMmk9KoNlIfuumUWM+i\nbOT6IHe/BLXWeUlPq+MaWs24FCknOFJCCDBrGC82Pl7cBXUEmax9+XGaFVJGOCxHkXZcja0YxlvM\nO23WYePPOwvDcVxf1FLuOm8b3FG7QXtIjpFDZdpojebSScsfyrChdf3QQRftrU9JoEE9YGtEpQy8\njEF7iOov6lR1h7xky4YqvJXL5PJxh2ejVJkbnSS5dhzqwci1gaVk9aDLA+at0Kdhi3IrJhfyW/o1\nci14qtUVNnut64e4OzJYtg/ZJuQoqDN+gwTSScsv5KdZIQVBoKR/dKQ2bSj1QsYLqBUD3Uv6NY7m\nDOeyhnOYfRaGvJTxuM7lHtFSxibZ1DpvI2xRO1j9YbPncIzoSvdus5iQYrb2d4UADynqxUjaI1Cm\nv9nU0juUksqvdHa6g8PhzqObyPdQDYItbzo4VIs5Ybsoz2KlWs/We6eTruqPdSWNajOVZB48Yx50\nIM1bcSylm1x6T6uRitvmlulp0aDswwxVdJL76XGsk0ZHVKEuEnpclJAgJz1vTv2l4DQrpFRkLJNF\nZtK9FMTC83O6q7SACgGM5MeLza41nrF53aNkKbVJNkudtxFG+9HR1q4jNTMnm5DupZbfeDRiOkoR\nvDi9OGz2W9cPQR2N6gO4EamOvtyuhBC03vngyJvqja6eNl1FDzUbrS4z6ar2WFfSqEZTSXaP6L0o\neVC9fcK4lG5y6T2tRrPMGLVT0qJK64LQmBVTD4K3nh8n4y53X2liFE7nVpeItaaxnKUX8rNb9p1R\nGwkh0OuX5TJjd+G8xc0ylCrw1GZYx94QHqFd6Wc1I3Q6L3GCGmulvclY8+pG+lm19wkSxqNVDdk5\n6J/H8RE96/evHngSgbRyMVWHIyGvtzSQujJS2NlKbLxkugoesmDMU/ev9d4ZSVdBz0pSZ0yjJiTF\nx68P2kMlMUwHYbql2XkrBIVE1WZyyT2ttmu8WY5wuZFOqQ6lHzBpl/odlTpSAoKWVHwv8Anbi9EH\n7eHyC/lp9pCCIDC2qQtL04YN8wa1FKqhBeJ18mpyFXhqM6wDSrBCp/TPDjJX56rzNoLsRzhGwlTz\n6oDtrCqgFPpKRC2ywyHhKN/Ck73SKO88uomnG4xoRETJN0UpKQq9ilsqgbfS+aDnTfV4HQED+nAv\nW3ctjRMUdpNLqX8zOveKZ4Nzp4uHHC2wnQI5SKiPUNEvc1wjkG06nL47Y1pUF2NyRhP/ZurgjqWx\n8UrxvRDCXdq+EjiLHlLGpg0CSINESufoMchV6ux0RbMPbWTLvWdcDRvO0gzrWIcstYWjiAA1yYL4\na2H/b3rY1vOdnW5COL2A85deJCYSvs6V6xNcGFR6h4AbPliaboDsTtjrj291p/I5OrIFDHT5l4MB\nWM3WFUetyo6GU0/iApfrC0zb6EW9eDya2KRXdpKMnpaQDoK3nnMcqEqjFDb7m35eH6Eys6vyOrJ3\nbsavqH9sb2UsngJdGemkcXyEsfHgEVa2jWamYq0wjo/2rx4sMDdgSXCaFVIQBGH8I/31ubSRQPZy\nfhYixMdb19tCCNk2n/HTJa4R+mGmAw60Xes5IUTnVvckvoiQjqvtrGaEXNeLoaV4XScHc5OvHBeM\n9K0H1Q0alZ0FpJP04zqOj4rBG/Pe/aXDJuHQRqQAFC/KSyYfiqTAGpkGRyLQKP8UCxVCUFWxTbyj\nflz0C2Gzp4u3EMLz89Qu4ygvIhI5m/TKTpJjCgMicuDGNl4gkmPYun4oz+dMPo1jOYdvR5MAkwsM\nci4kvisFNjGGPTGIh/j0HGeEuIWwjlEnrYSQn2aFZESWpo0Xgmnnx34V1WL0ukIoKaTnBV6RO92S\nC6a0XWGzDytJmJSZkX1SiVOD0lg/qzrN5fH2JKWin7TW9UOacZAo1Bn+EiEM9JTyrXdfaUJTLuAh\nzet3ngITMhWta+2gvE7aSKcakeH5OS/Okb4x8jTafFBEGoq1QtQbKVOXhCbeYKUTFvGWXznWbSaC\nO0wRpItNEbkSxbKMe6afo36MIZz0KyNRHl1glHO6DCO45E/seM+9uHW9jcJro4NuFGPKNuHWxvCj\ndPExbxB0UkZKzGXDKVdISs5AsRwzwkvmX82V2wDnfFD2B4dDOeur+EMZ0brWHo+OgpJPlpRMLYx/\n2tgnj++4np9OyB3lsKDQDrb+FJCVCp00BNm89fzCIUQAnwy1rcxFpr5YQshoQo7jyde+vtSTNG3Q\nJdxLJroC7oAzNeGFzT7iYPocWHryyhKLhBNSHQN/SJUpRvGeBpx7I8cjkubLIQWri7fMfwM/SZik\n1/NzZL0JZDol7SIbc2I2eaPIuefnoBrddhKKO8DOZzvRiGzbgsa2RhF8aDhxIK+r2N1HvZ4+bPYU\nnbQSQn6aFZIyUlOxHOeCPOgsFSgVo+edXvwzL6BpEB5ZQJ/JRivmIiPcbPRXsm6pH+MpdpIaQiEF\n+r35eVFTZ+rYsNImpAxdwqluWIYt4Cw3zHrtIQJHxjmwxMmGf8Lkp4STm3gXHKnF2hW0HNmkhfQi\nMl6OujIhhEp/nGRZhBDjEQjIJ8Wtgi1UIITApAxHlBLlFe6JMFSkN46P5EHpyt4oU0VpIVnJKa0L\n49nZsoP2dESsMtld3YlmyRl10vLjtFfZJc9i3XKcC6j8znJlZ6eLZjf5b084jw7Zo4XX8ZKZx2DA\nRHEEzvxi2ghB86DsO3jGMq4jl1QhJ5FKu/lCAAICY2//CkGWcLwX/enjCLgpk5OS6w3kI7L8g8FB\nLn/wkhHg+l2OOVKdNHHwMIKy76aSQ1GczqpF4p14Ofmg5Hvr01d0OSceWMe9UNGKLI5NTqhIDy3e\nxrOpNA4GZb9+dyts9uW3IGt6pQmPVLjn7KgzvlisXfH83GrV3Z1mhUSwWY7ZkfHB3brWFpr5JpwE\nkamgsyqSyp/F1hHHRl8Kg3L6OkmZr/u4ZllHKdMgowGfpBsndM5knbS61EHAdMCxKXzqmZiB9CY8\nmUTY0+bAkvyj7V8vzbeRblDpuZAGvCrXIASH4+mgkiOuICNnDwGKJE2x9RAldtDWkf9tpJyQ9yOg\nxe9UbfR9ih3sJfyz+GwhxuO02bJ0F5tO0p9Rnp8DbzJutBJCfvoVks1ynAtGzm8ZkCdMvDf8+aJD\nu6m0Gv9Evd/CuoTamNzHNXVLcqzMdlzTN6NRtgB4Ggbl9dTpHidvKiITcvknaTqA+i7XwN9ZZiBj\nE55eSurNdNSNQCKseP/yxToxnUL+hrpTA++UFFby7FRycO6F8zRRDA1BMBsVJPxyzz5RRW68peo+\n234A7Er/BIwV6vTZkk4ix0jlUJ8N6NGUoxmyCXunI3QS6IjGoyNWSC8TQRAgmnzCxLtIq/yGPFUa\nJUdIcDEdIGsj4YyNpEJuSncc11Qo59B2XNPXcTb5Vhrl1FZWVHnMe18ZZEKuhPGoA0Njo97ILeGe\nxAw0VxMeuUrj0ZExeSNDebjLfg8BjpTyMBVJRT6tY3S2ZFfDdpoohuaIEMqCZ5uooqRkIGY6CZ4y\nt0WfqeFg54LsoWoco8qNV+oFeDTlSFnNeBeROGRofLZdszw4zQoJGI+OlL70BdexfJ1yQZ3jz93x\nASP0syrmGSOkQGGZXNhJ0s+h8bi6obhZRhRrhem0ZksQfOFeY/pzZH1PEgV96RjHk/HoCPxStms8\naW6sfXLSNGNhXgHVa6MjzJQz3subJUpIisSUCnLVkdLnQxpzpQpXkPE0KUJlixDK1xgdO53iwUsI\nU+Rt665PYpz1bOsAUEIgB6KPy5jqsz1zUJhK9fEOvhII+aD9CR4ay291nWaFFARBpVIp1grFrQIx\nD7qPrg3IixppiTFIKSPT3Vy3xpE27MTEt+2GrgBsx9UNI8WDflyzrJNxTK2R/1gsqo1wPsNmD+yT\nQghEWev1+vKfVR2QcIwpinoxOFUxhHTmsiTg7G7CM5aSyt6/t56HqGPgaetaW5FDIt6lWgZ9QdkB\n6ux0je2req5UcTWMkT3dd4fLIl+jk+DpDpmRCcmbpcy3cg6VfKIAV8oZiPVn/+oBPqXdzxugUbcF\nAxxGmzLlSNFndC9wZAghKo1SvV43LrVUOM1l30KI27dvb/8X36zfK8t96aDr9+xck0boxxWZ5Owt\nltTOneVJipNj3JvC/JgFugKg4zpXXYCDjgXHNWOubtAe7n6eiYsJ++zsdEPRkx8B2SfwiqlN+knU\nG41HR956XqESb11r3/4d82zG5ceNGzf2/vjt+r0aIjlU2T++1cU7JWag1CY8TyMRlr1/POPG8RHM\nc+UoIW1D2R3HOBJPYu6xiQHlSrEZozuih6301fQTF/VjnW4VuR9IF0w3Y2QSDF5u7iIv4S+H/sbn\npsgeLS5XhE/78DRaWweo/Ae6n26E3mFUf9C32brWvvE7v5Nx5ZeIcz/96U9f9h5+hoii6Jd/7R+Y\nWDQmOLqyoDi4RkSSfiRxsRXUuZGxwgJ9Ho5HNno7suuS3Vea+mrobczO7TZoDweH1il82ZMTC5SZ\n4LCN44nMCS3/0/Yn8vm0fb+7rzRX9xQ4JBwKAz8IITw/5zaeFAlHWEkWD+NnTjdCxwxegeFvkyto\nLHT52KRFvpeN4EA+BTahkl/HvChDn1Y8IUIp6FebVsARAHeRo0c1bPbQNo7EM3r+dFNA2fNYo1rv\n7HTBhm68Ee2cuoOpLFC/clWE/JR7SEEQFP/+r8hjFwBqXJC5JjvtKTmbTQiIRGdeW4bgGNssI2z2\n63ddqk6Z2uCGbeS5N0vFnwr33FvkpRxdhIRUJkrj4gon/9hEHQ0lJIRw0FDqm1mJUIYNkHB9AIQn\nEda1rrXxfEQ3qC0wIHM6GL1/Gq1ivNHmfnWasYiHyDbRBccXJzwgqEQfj6ziRPeyZWJEEtnDKbAJ\nlXzibMyt3izvsE04x/HEW8+B92HQHlJQUefTop/dLA/KvfRggC2HJHtdIjnIjlO8QkJ+yhWSSKJ2\nDq5uz8Q1qcf0gpIf9vpo4HAMHXHDmx2OYoStHlrGXNE/xxnLqCBpHbfqKtYKCk+ScZGFicanMYrr\nh+ifpdfdETk3BofD1Y3XAZBw22cOM7zSKI3jyc7+TWNML2m9nFr06NvTFTlZMHYH4hMwf0e9ePPR\nseGf/HDMbjcdNiEdNPxfrhHHSXEQAVNkLxlCaI6hYc9ImgZlK7c3uojkdeQ4isKh52CuE4mbhfI5\nhwtoS8cO2p8g+i3XkdoicriXmJaHWL6X1RHyUx6yE0JEUXTp0qW5Zr4JU0wPEfZxPJl3KXU/vdjt\nRuy+0sxyC3dsgZAa2npR6wCpYcD9qweLjZkg4AMcxxPKZLgjcm6sSijDAYeEU8OsHJUCKDAwrb8q\n+Z6fA62Uw/vX17Hdy/EtQ0fSJEYlukiaCQMXgpLv8HEhlsgMOSrNMNvCHf6CH7m5X4XihANEcTD8\nOWLp0O6Os4AIOfxF2+FyHwTQj+Eu8uAJoUXkdl9p4utw3GuFhPz0e0hBENTr9aj/o7meVnpMDxT9\nMHxEmgfj2s/sxFUF2ZNDcG5SFYk+NPNntA6AY2MLAy488ZZAGREgNSLnxgqFMhxArZ1ujOOJhs+H\naqln+H5mAwPTfv7RkRDrNvm0ufiyU0UlcMYVoAKJqA0NqvJOhBCkn7Cf/asHDm57xPTG8ZGD1ByX\n4Y42GvvxlJJ1WhpnVPAJF/AVVDcY3yBFyJPC2k9a19qKlBL5lnGr8sawH5vHL8cbUHOh1P6IVRPy\n06+QhBA3btz4rW9+4yREdqDop7n3iHik2lw2yLFvGUmxbKYnrP6I0eGIvyvrpMbZ4CNm2Rii/8aN\nOcavuYGnGNmJICuDk7TAaoSw2fvT/+Gjk6ywJNDj0noFiiPv6Pm5QPj4VBEGaDXbtmyTUuRpTKk6\nQsFEJmTLSAkhoJ8G7SFCiPW7WzZu++k/R0dZmsmi3sjzj6PcCr03COxRTm1bAdFvd7pUjpBPc5+i\np9RlGOOQCMpR9yEOpq16PnlHMxaGsR51heJ14owoJHBQLkx9Nk5IkT0/37p+WKxVUWQJt+mYFzLz\nwxHGnb4fmfgrC1JLGzIO4kutI59rdLqXjO9TjivUbfavgCrrYNvKduJus7mzf1OcbAIs8uqVSmWB\nv102gJSEJCrqxcoULpHkHW0r0LADMNOjQmHQ/oRsr+NkquTijzVOPMBm5cjRhVRLCPxG0zmQdk5u\ntAa7HeX9qwcoyHaIH/w2BPdS3RFbutSYIq00yvhgIatKnEAxthDHQ9/kzqObKOSxRfj19ixdJ0X9\nuN6rOz6cpcJXdnd3X/YefubwPO/HP/5x9G/+7wUUknzk1vLnnw6/jPrx5eqra/nzFwsXiluFy9XX\nxDkR9eLu7QdPup8ldS+ucRVr+fPinHh48Fh+yiMaXvn2HG7cWm6te/tBUPKNt8NZzbKg5+efdD+T\nwyAyol4cvtN/871vZN/YxcIFfBTyB97Zuf/GzdcvFi64/3YcTx6++4Ow2e/efiDEuYtXfql+b+uN\nm6/j8xfTWHm+uFVYy5+/XH2tdf3wcvU1/GoudG8/qP7D/3Rzc3PeP1xCyBJuS1Ku5c/bvmW0KEGq\nn02eR/0Rfgb99uXqa+PR0aD9w/Cd3tPhl88mzy9eufDw4LHn5z787Y/efO8bxmMVlP3Ore4bN1+n\nV6aG3b0t+rI8P9e9/UC+RtlScevK0+GXDjum+3ZYaZSeDr8U54RNtKAFYSQZ7yWE6Ox0cZyfTZ4/\n6X56ufqqfs2Hb30E1SK/QUX2lGsIFwsXLldfw1yJJ93PgvJ61I+jfty63o768cXChc39r6PBGX/b\nvf3gcvVVsJU/mzw37nzQHq7lziuWIr41fDuenx+0h29c/E9WSMhPM1ODjBs3bixA0KAbgHpf99Su\n2a/W726BEqJ1fdqM7eBBUIgSjMRfqfAsbJXAXPExBx+5O5png8LrBYfS3VEBYxBhnOJWYffzRv2e\ngeBL4UBy8B+7EfXjGzduzPtXSwtIuLsp1cgXpcwJ0+nm4PLW79WIpgHRrdb1tiMt72mUIjqZkI0m\nVSZ6cPCbkL9FDBFGTLm9nQTHRF5nGySBV2bpaKfpUnk/jhQpnVb4Q9j87ueNnUc3QTyvvDUi6EIU\nUefUNzJKiGPmlD4c5dUS8jPhIQkhgiC4/8//V/HVn7h9FxkIjm/uzxw5mJlGcww+0+Xqq8XalaDk\nj0eT8J3+w3cfPx1+uZY7r9wXVhVMUSHEh299BBN13vfl+fnwnZ7Reno6/DK7v+Vwkj5866M339uc\n1wWBrU3GJll8ymXwh1rX20/uf3qxcOGNf/R69fc3grLvsHYVq9Dz82v5Nd1WdSPqxQ/ffdxqteZ6\nU8sMSHjnv/mfbS6LEGItt/bw3R/I0oJihOrvbxxfI4UB1D9PogKen386/OLZ5PmgPRy0h88mz4Up\nKiA7QFEvHnx/+OZ7mql+TugeSWfnfnVvAws6HLvu22Fxq3CxcMEhvTNxAi0sQdcIIfA63qPukYTN\nfnHriiKWOH3YgEjcNX0P5PQPvj8UQjybPK80Sm++t+moQsTnTK8EZf/p8ItBeyh/UJ1bXVvcAn7S\nh7/90TierJaQnxUPSQhRqVQWoJKzEG25eNtQnldplHce3UTU2EijRzSpDuKvVOh2KDBX1me6H5P5\nfJK2IZAZw7SULT68KBPK7Ty6CTsxNaaq8IMlNzLwH7uxWqVHGVGpVDw/17nVhaTpZr6n8Z8KE7uB\njW8bwHcHwd7cr27eqY7jSedWV6fRk50Sm9+GUIH8CsqXZUkwjgGT2ett14jZOIGN4FhxNQLTIAlj\nnMCTxiDpxbeK019plNA/t/PoppGeUb6X/jRQpu3Z4hbE1ojpLSsn5GfFQxJCBEHwB//lH9iCyAoo\nqq7/CuaYI2YtQw7Ei3NicDikQHxQ9p8Ov3zS/fThu48371Szu27aftRA/AJZH5GYz2TuAbaYeKYF\n8+fxfHw2ee75+aDsU3JIiZtn9GwcWbGLhQu2ULsR3dsP/tkHH3qeN99bWnoc/umH9btbSVIzhKP8\nbPKcZNXzc/ASHDP9HGEASlDBkRrHkzduvn65+uobN183pJoKF+CUjEdHa7k141eDdZ4Ov8CjfBxP\nTB75OT1XqqUkzz3pfqo4SXDLyP9by59fy68pTpLxsARlv3v7AfncSFs6ngbIDMFdA4uS7vR7fr57\n+wFcH6R5jLkxY2ZITE9T/unwC9T3d98OL3/9Vbz9cTyB/9S51R20h8+O/p3n5zb3v/7k/qf/1d5/\nvVqswae/MVbGxsZG8E8upJrhiKq7qy2zcOQYIXN/4RV3618WKN1LqTSaNii1wuiTX+xtEmCtT/vk\nnU2XqUhtqs3YvTtoDzs73VMp+bKEIw+kcFigvhkNDA6pMzbAKlZ2LnEAACAASURBVGJva5I97tsb\nHXnreThADu4MeVnb0VO+WSPZo17prh8EvWnX1hguE9+5BY8I5VCqjtwSHBrlSjSxEuODMQaTei8U\n2aMGz8HWuKJCfibKvgmVSqXT/r5bISGq7n5ouptb3aA2QJCzodkCxF8JX3Ju3mWLWwXqQxxLFMLz\nApXBcvXwAsqDCOVwVPCi5+d272Wi97YhS1MtPtJU0vGoF7///vsn2czSQpZw6peUCRsxjIAIflJL\nEuhprhthnoXinSR8etN+LISgcmq9IVQpNzCKnNK0ZBxfokuvfhCSZtWh/OA2mlxByR8cDsHtrQue\nwipEizsIkRWuICrRrkiBPnfDLP0hbFkU6Be3CsbDHvXilYvXibOmkG7cuLH/a+84LgCHd5Zqt7no\nTY2AQG/uVweHQxCEjEcTNKiDZwyR9Cz6SW4x0SeeZYeXTKQNEsLKLB8Fnjvj+IiMNTx6Ko1SUK7B\n5o16o4X7wICMWTHoJAevl0BJ1R9UFt7JMsMm4aQkol7cuXWENB7MeZsZJHen2Yr33Kk7z88NdoYo\nLavf3YJGDHv96HpbuS9OE1i0bUvJCtI4t0JRNjbplXkgHSlSLxkk4a3nUT0rhCDqXpEclqC8jsum\nQ6fsRhd8GuUWik5yNMyKhDIYLeGpwYaoH//p//4/WXezrDhbCgnUyA7OD5F5ogQZUIs9ZOmEe34e\nWVxquBOJ/QX9hKcG6Sdj154nsV4az2p2wBTFGbAF/XTSSYSDoIHUd9qP6/dq49pEMQbngmNKjfEt\nDNqf2HTSoD0s/v1fWa3Aena4JZy8nNa1dlD20f0qD4+QlYRekqCv6W5upfhb1BvRICWh8QNF19vT\nzTsHXJGCtLHXC8lJQguOUSHRYcFUSUfn+LSBvR+LJLJnZBWC747VbN65TfPJOkl2xXQl5Pk54ltC\n9LKz041K5i96dYX8bOWQhBCtVgsDzZTXw2Yv6o3minTpMeuMIG0EYUpN+dhcENm7x5o40vP2MymA\nYo76Me3QpoFSwwtyIN4WNM+CebNiRj4benff+vq3VzGakRF7e3udH35fl4Fk2t6W5+eMSVBdOYEE\nQTjHKNjyqQh9uwcRyffFE59mCBn9NuRKW9fbjoyU3K/juCP4G5UUqRJtpmQPBuYalxKzU4tsWcws\nWSjw9SE/RGdcz0VRwthxoFZXyM+cQjIONFtMtaSyGps3MKuNxLSOtp/97jZ2ZBwGUBzN9Ua09Y9a\n19uwB4m5RyTe21xZJUWRpHKBW/Yz2b96MK/bZ9NJu680/+qv/moVjceMMEq4LnVuGl8qTCABc8xW\n1peStZFwcoTT9UF5HekcOTwwHS2YhAegLNGHbluKSgzcI0jA7Y22IYept3/1wD0kScyWKgiTTnI/\nXojCjgJxxoII41I2nbS6Qn7mFJLQau3m1QcyMpZ1EYzcX6nH1b2gSKIfaLBfrGfIuCxyUYuNdQD0\nSbUL6KSMAzJ06Dpp0B56g4untaKBoEi4UepSjTD8VbFWAMUGSvWMtI2Kk6RoI3rRpv/oeuM1evlA\nquRkOQXjZMqqw9enWj7HMTc6f/p0af19KRR2g2Q8oPto2OoG5b9aaSE/Wzkk4MaNG3vNt+tJKc7C\nBdxCyrhkeby6mSjdeXgbvIQd2VvP4biecNqQSM5hUPJPooqEvZewfndr3tHpi31BFKAf+ENKzn/r\n6yvDfLwwZAm3SZ1Sk6YAuhze9v7Vg6DkOwiF5aJTW7OtrQgI/a3Qi2B4M5yOZBBM61obStF9UshD\nclwDpyR10CreoIPA3viinMWUG2ZtfMGwiRUOVn0/trpB5UCttJCfIaYGQqVSQZz6hNpISAnS1Ctt\nz4Xplhol1OMuDARkHNR22YGaWge7XdZ17FxbOEJZCOiQwV7Y7YNOQvmJwFs7FfTebpCEk14x1iNU\nGmUju4EcCJp+gO2hSOrKiNQu6sX7Vw9a19qoygmbfUezLVgS9NdBiIefi7UrDunFN4hqPWgp43/T\ndreSP46PHJcN2kNwTLjumBDcQWIxFlK5BlpN/2zBSxI2e4PDYVBeD5u91rX2/tWDqDdCdbhMYUdV\n7G7OERvdJb5KOlArLeRnUSGhEils9hw0lNnh5lkB3NpICOH5eSOlY0a0rrUR4ic6opMAND+wf3VK\nx+xwsKkqR8i9mYUbaele4Jrs7HTr9foqBtbnBSQcrZGORJGNSkf5KxqSRBd4GqEwOEMdlZBeMr5L\nflGJZRmvAcBZDG5WB0eqQHtArWBjEppek7T7oDTOKISkg+W3bOQTslWNY0ph1I+JK8/GFywLOWoR\n0ZiofAKOA0WaDJxYqyvkZ1EhCSFu376N6cgnX8rzzWxyBIeVKi+CYP0CG8DhJFPOvZlUyGcMZHSL\nrZbKEU5HyKGTTsKkpwBG8a//+q+ffKmVwI0bN5B7S5U65ftFlkL+K0cYgDQTDHwYXgqjHUEhSxwk\nUyHka1DaoP+tTHPsUDY0c4tGjhkvg9ISNLvLZHXpXeH6cbDFAEAo10rK2SHqjrFPyq9wsaKTUvsL\nwdTQ2emutJCfUYVEU59Be4qww8IOCuws46+y1zrrj4YsIMuRXknlfnVDZi9NfAuzCZl9HRtSdVKW\nRWyYPhSutUHhOo4nlUplFQthF0OlUsHUPrd4K8MmlFEUx6s5wwCD9jDqjZAOQSYDXKuKPMtRu3FC\npW/cj/Ii5FkSS6uyIVfD83OgL9GvUQZFUrm2elk/VgxW/TjoLsugPWxdayPmhnKe+t3aAlSq+sgJ\nmZ5Yhizng/YwCIKVFvIzRK4qw/O8SqXy3ff/6M33Nou1K2B4fNL9LHynl3HIngwbGeWcnTfn4LTN\nVbSNuRXFrWNJdU/bc0NnLwUfZdjsz8UdjuEOWYoPLxYuYHiEcYKGECIjWSowTnj+O7e6oLb0/Fz9\n3tbl6mvd2w/ef//91Q1lzAvP8zY3N7/7/h9t3ql6/1HeJt7ysAl9FAUBEm4jA0W1Hq65WPil4taV\ny9XXPD8PKmFQ667lz8vH5MO3Ptrcr168Ypjhokhv1Is7t+7v/MVN+Rrj0AoxHZUypUldy62F7/T0\noST6IAlQqcq0wjgIb9z8FX17JK5gQcUexskUlafDLy5XX8VoCTpNC1CpitmRE8pACl3O4acO2sN/\n9sGHKy3kZ1QhCSE8z7v49776B7/3nUqjPJ1jtFWA+C6gnDzT7MsP3/ooex/oWv78OJ6ABTzjW7BW\no1rmvqSCBszMbCy39qT76VzTx8NmHx9plottRN0ZicZtSghDZrHnD9/66E//6Uerm+ldDJ7nPZ/8\nuzAMK42yQ7wvXrlApOBvvm9liMdTW/mO1LaY0RFNm6V5yk+HX3RvP8BUMHo0j+2zjGkR/LOzc39z\nX+XCNyobPLXpD22DnWSlRVeu5dfkd/fw4DFxaSugachPup9d/vqr4Mj/8K2PgrJP7PXKIjTFVT9E\nbiH3/Px4dBT144fvPq7ubQzaQ10JQc49P9+61v7d/+wfr7R7JM5mH5KM7e3t6Bd/ZEyby/2nRJbs\nqIQ+OeX2XFV/iNcbu/9Sayhsd9cZlGnBuVqAU2m5dYBnlt57ll5CmedY2Dt2w2ZP/OD8gwcPsm/m\n1CCKou3tbfH6c/3DUdqrhRCVRsld6K+ItN7AZ+uok3s/Ia4OIZcXcTQA6d1p+1cP/v/2zii0rSvN\n46d02QSWsS8DE0LXYm6ZlmTHZTEzsKkFSxUGNp6nZojH6VOtnZBh3lap87IsrNyw7JtTl52HBc/W\ncmcfarUhyuw8qPTBSh6kpDCJukRDZungWyTa0tLlWlBIFobuw186OT7n3KMr2UmO7f+PPrjO1b1X\n8rn6n/Od7/t/WsK0eT9JWenaP2m1ruYdomeuLBi3jj3tJNaqOIeBheiH49QUx6Q/ULPciiv398Eg\nP7grJDA1NbX2y7cP/+Wfm5OUhx1gU66clHXJaA0ghoq2JQU9hNGONiW1pYa1qauwTSEdpI/XqYTZ\njLpOMtdqaVZC1ptpvvmHO3fuDHUz+waEpl+/eMmMXMnh3Sy3gsx43OkK8VTU6DgCA8H2DrCVC9Vf\nfPCqdk7rAMYSAfdwr/pHtJrFmuz+1gPzYJwkbndrlxv5K/aSmqOTR9QB2VS6vmqnUmPp1eLG6eUf\nW/tvHZ08gvKgqNExw2iIXtz81e/QdijudIUQL57/QVLjVzMWZ66TrMsjbZwL8VTc6SKHNmkthY3k\njY2NfdDf66ALUhAEx5/9q9d/8S/ur9o04nR08ghahFUK74/WjkgIEXe24k534NoCM0dHh/Kk1uYO\n3vnZtaRnVQhxdPKI2kjNeW9DxOtUoEl4kpvvwgF9FBFSqRTeX/23tT0dVd8hMjRtHQzYN3pl9eUg\nM37v/Y9/8cGrjrmXnDDF7W7iUj45XHy/+wD/FHe6sovgveof0VZumz49JW6u3G6+23I0rtTEr/rP\ntRfP/8DdRt0qWuoJkY4hhAizmaOTRzD8kPpULW5gBB4eP4QUj+Mzz917/2NT6cHNlds4iXaJh0HL\nTlc+wkl7QtipOr08g8hnc3sLcwki0lNTU9b3tbc46CE7kORHORAtrCdSWDEOPOFAG6GUkb2hVmkD\nowcidY6GGTkZCjT0w7fewHCcm9KZcu7Yj/aoh8ruYoamzQiSGc4yo9ZCCIzzpOHniNph8MD6QY0n\nx9vNv7HDJIQIpzPuwSZjho4nQh20bvs+efPwlEtyMQbwxGomd7B0BP1wS/LztLbXA1rEUgtry1/u\np4j0QbQOMpmfn6/9fW2EXhJBv82M6I9m0U/RcZhRuk84sPVfynpetZ/NQNw+/PLecE6HFmrlhEMh\ndxrw806aaAikBX/29GqdaiSEEMVi8SevvizHFb4TtfkKUvDVsacN714f2HY3yIwlOV0lDWB1KoOS\nO/UqQgj1Qs3yXbRHgslv0vatzP92VE8j/7u21MgJYeYUxIaNvXyVo5+kYik0Gbe3sJVrHpCkRs3y\nXSm6p9+YMTu2ALwv9cx4j+qEL6q3oyufbW5uJt3qnuOA1iFphGG4urpqtQZJSX8ilsVGa1IpRqqb\nSagNBNKUIcV5Mu6adkkzRTNWeU63fcNoTWZrS/XlEyuQ8/x7c0KI3ML08omVnfw5SrNlro0kYRi+\ncelNxKOQ85JbmNYmK9Igx3oGfANKKzlHDaxWACuMYtuBJXe1pQZK6xY/XZBmELWlxuIzS7goFvRS\nbNxV2Kh/glmc6GcKSC8fvF/YKODb//TyjOZMYdzew/I4axGrdUKJ62JUYz0k+7tbSeqIqJbu1ZYa\n+2yQc4XUA0/s6wVLq6SBqElozfVWMDE2NTeJEj84UeJ/U64btG7NKqopQ6pTpWtrm7IZq7w9fCNY\nvwKk/Vca5FwYKi6bgcq0pRF6VYBKobq4uHjQ8rzd5HK5wrnXSmf+I2q0kzIwETuylqyiYVjh1vna\nUj1ub2GHr1m+iy901YlAs3UwQ8dBZjxudx19Mk8vz8BfHMeoiyeheNvjeETYBs781D57akdj9RjM\nzHCtSqGa1Bo8bm/b5ZULFzVHVH0KENkTQkzNTWLdj2CpfNLNR8Yx75yamwwmxtA/KX/q3D4b5Ac9\nqUElCILrv70RRdFQoTZMFV956+VeMKSflZBUijEwgy4pVSlud//9735t1mS4TjV2uFrccBfbRvV2\n7XJDq8xw316YzVQuVM3t3KRyQpO43a0WN2qX60cnj6B6Q27/3ly5DcObMJtBEWLSvnESzXLr8Mdj\n+2zmuCuEYXj9tzfiP/3v560vkwrs0GtVq/KuFKqft76UX9DN8u+nzk7K3DmtBjbIjMkBbN3IdJTc\nYdekV5xr5EeguhYpMy+e/+HxmeeFEFGjE3e6h8cOxe1u4n+d7v3ug9zF7Ctvvfzi+R8im9R87zK3\nExl31to7a84O8nFQPy7z69Rq2am5STUf717146MvHMGnd6/6sZYrhBQP64Yuztk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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "[node,elem] = circlemesh(0,0,1,0.25);\n",
    "subplot(1,2,1); showmesh(node,elem);\n",
    "[node,elem] = uniformrefine(node,elem);\n",
    "subplot(1,2,2); showmesh(node,elem);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1. Hierarchical Meshes\n",
    "\n",
    "Generate the initial grid by \n",
    "\n",
    "    [node,elem] = circlemesh(0,0,1,0.25);\n",
    "\n",
    "* Refine the initial mesh `J` times to get the finest mesh. To get a mesh of the disk, the boundary nodes should be projected onto the unit circle.\n",
    "\n",
    "* Construct `HB` in two ways. Either from the output of `uniformrefine` during the refinement or call `uniformcoarsenred` from the finest mesh."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2. Transfer Operator and Smoothers\n",
    "\n",
    "* Assemble the stiffness matrix A in the finest mesh.\n",
    "\n",
    "* Construct prolongation and restriction matrices using `HB`.\n",
    "\n",
    "* Compute stiffness matrix in each level by the triple product.\n",
    "\n",
    "* Store the smoother tril(A) and triu(A) in each level."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3. V-cycle Multigrid\n",
    "\n",
    "* Follow the lecture notes [Introduction to Multigrid method](http://math.uci.edu/~chenlong/226/MGintroduction.pdf) to implement the non-recrusive V-cycle.\n",
    "\n",
    "    _Be careful on the boundary nodes. Restrict smoothing to interiori nodes only and enforce the residual on boundary nodes to be zero._\n",
    "\n",
    "* For one single grid, say `J = 4`, show the decrease of the residual in certain norm for each iteration of the multigrid method.\n",
    "\n",
    "* Test V-cycle MG for `J = 3:6`. List iteration steps and cpu time."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algebraic Multigrid Methods\n",
    "\n",
    "We consider solving an SPD matrix equation `Ax = b`, where `A` could be\n",
    "obtained as the finite element discretization on a unstructured grids. A\n",
    "coarsening of the graph of A is needed and restriction and prolongation\n",
    "can be constructued based on the coarsening."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 1 Matrix\n",
    "\n",
    "* Load the `lakemesh.mat` in ifem/data.\n",
    "\n",
    "* Assemble the stiffness matrix on this mesh and take the submatrix associated to interior nodes only.\n",
    "\n",
    "     _The mesh is only used to generate the matrix. In the later step, only the generated matrix is used._"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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olluZ5bQaD6GYBO0fb6aGVs1yC2yE+xNvY3LbXml7Wcy/zzckQhKcecAKwZwx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\nCuo2e6cWXmLNIYgMWXZ6qvwiE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      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "load lakemesh.mat;\n",
    "figure; clf; showmesh(node,elem);\n",
    "A = assemblematrix(node,elem);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 2 Coarsening\n",
    "Use `coarsenAMGc` to get a set of coarse nodes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  COARSENAMGC coarsen the graph of A.\n",
      " \n",
      "  isC = coarsenAMGc(A) terturns a logical array to make a set of nodes as\n",
      "  the coarse ndoes based on As, a strong connectness matrix modified from\n",
      "  A. The strong connectness is slightly different with the standard\n",
      "  definition.\n",
      " \n",
      "  [isC,As] = coarsenAMGc(A,theta) accepts the parameter theta to define the\n",
      "  strong connectness. The default setting is theta = 0.025. It also outputs\n",
      "  the strong connectness matrix As which could be used in the constrction\n",
      "  of prolongation and restriction.\n",
      " \n",
      "  Example\n",
      "    load lakemesh\n",
      "    A = assemblematrix(node,elem);\n",
      "    [isC,As] = coarsenAMGc(A);\n",
      " \n",
      "  See also: coarsenAMGrs, interpolationAMGs, amg\n",
      " \n",
      "  Reference page in Help browser\n",
      "        <a href=\"matlab:ifem coarseAMGdoc\">coarsenAMGdoc</a> \n",
      " \n",
      "  Copyright (C) Long Chen. See COPYRIGHT.txt for details. \n",
      "\n"
     ]
    }
   ],
   "source": [
    "help coarsenAMGc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 3 Transfer Operator and Smoothers\n",
    "\n",
    "Use `interpolationAMGs` to get restriction and prolongation operators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  INTERPOLATIONAMGS construct prolongation and restriction matrices\n",
      " \n",
      "  [Pro,Res] = interpolatoinAMGs(A,isC) construct prolongation and\n",
      "  restriction matrices use standard matrix-dependent interpolation. \n",
      " \n",
      "  In the input, A is a SPD matrix and isC is a logical array to indicate\n",
      "  nodes in coarse matrix. In the output Pro and Res are prolongation and\n",
      "  restriction matrices satisfying Res = Pro'.\n",
      " \n",
      "  The submatrix A_{cf} is used to construct the interpolation of values on\n",
      "  fine nodes from that of coarse nodes. The weight is normalized to\n",
      "  preserve the constant.\n",
      " \n",
      "  Example\n",
      "    load lakemesh\n",
      "    A = assemblematrix(node,elem);\n",
      "    [isC,As] = coarsenAMGc(A);\n",
      "    [Pro,Res] = interpolationAMGs(As,isC);\n",
      " \n",
      "  See also: coarsenAMGc, amg\n",
      " \n",
      "  Copyright (C) Long Chen. See COPYRIGHT.txt for details. \n",
      "\n"
     ]
    }
   ],
   "source": [
    "help interpolationAMGs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step 4. V-cycle Multigrid used with PCG\n",
    "\n",
    "Follow the Step 3 in part 2 to code a V-cycle. Then use the V-cycle as a\n",
    "preconditioner in PCG. \n",
    "\n",
    "Test the robustness of the solver, apply `uniformrefine` to a mesh and\n",
    "generate corresponding matrix. List the iteration steps and CPU time for\n",
    "different size of matrices."
   ]
  }
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